research-article

On the Theories of Triangular Sets

Authors:

Philippe Aubry,

Marc Moreno MazaAuthors Info & Claims

Journal of Symbolic Computation, Volume 28, Issue 1

Pages 105 - 124

Published: 01 July 1999 Publication History

Abstract

Different notions of triangular sets are presented. The relationship between these notions are studied. The main result is that four different existing notions of good triangular sets are equivalent.

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Cited By

Boulier FLemaire F(2024)On Formal Power Series Solutions of Regular Differential ChainsComputer Algebra in Scientific Computing10.1007/978-3-031-69070-9_6(82-99)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-69070-9_6
Eder CLairez PMohr RSafey El Din M(2023)A Direttissimo Algorithm for Equidimensional DecompositionProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597069(260-269)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597069
Jing RMaza M(2019)Computing the integer points of a polyhedronACM Communications in Computer Algebra10.1145/3338637.333864252:4(126-129)Online publication date: 30-May-2019
https://dl.acm.org/doi/10.1145/3338637.3338642
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Index Terms

On the Theories of Triangular Sets
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices

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cover image Journal of Symbolic Computation

Journal of Symbolic Computation Volume 28, Issue 1

July 1999

310 pages

ISSN:0747-7171

Issue’s Table of Contents

Copyright © Academic Press.

Publisher

Academic Press, Inc.

United States

Publication History

Published: 01 July 1999

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Cited By

Boulier FLemaire F(2024)On Formal Power Series Solutions of Regular Differential ChainsComputer Algebra in Scientific Computing10.1007/978-3-031-69070-9_6(82-99)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-69070-9_6
Eder CLairez PMohr RSafey El Din M(2023)A Direttissimo Algorithm for Equidimensional DecompositionProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597069(260-269)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597069
Jing RMaza M(2019)Computing the integer points of a polyhedronACM Communications in Computer Algebra10.1145/3338637.333864252:4(126-129)Online publication date: 30-May-2019
https://dl.acm.org/doi/10.1145/3338637.3338642
Dreisigmeyer D(2019)Whitney's Theorem, Triangular Sets, and Probabilistic Descent on ManifoldsJournal of Optimization Theory and Applications10.1007/s10957-019-01508-9182:3(935-946)Online publication date: 1-Sep-2019
https://dl.acm.org/doi/10.1007/s10957-019-01508-9
Jing RMaza M(2018)The polyhedra library in mapleACM Communications in Computer Algebra10.1145/3177795.317779851:3(86-88)Online publication date: 4-Jan-2018
https://dl.acm.org/doi/10.1145/3177795.3177798
Monagan MPearce R(2017)An Algorithm For Spliting Polynomial Systems Based On F4Proceedings of the International Workshop on Parallel Symbolic Computation10.1145/3115936.3115948(1-5)Online publication date: 23-Jul-2017
https://dl.acm.org/doi/10.1145/3115936.3115948
(2016)Involutions of polynomially parametrized surfacesJournal of Computational and Applied Mathematics10.1016/j.cam.2015.08.002294:C(23-38)Online publication date: 1-Mar-2016
https://dl.acm.org/doi/10.1016/j.cam.2015.08.002
Schost ERobertz DLinton SYokoyama K(2015)Algorithms for Finite Field ArithmeticProceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2755996.2756637(7-12)Online publication date: 24-Jun-2015
https://dl.acm.org/doi/10.1145/2755996.2756637
Angermüller G(2015)Triangular systems and a generalization of primitive polynomialsJournal of Symbolic Computation10.1016/j.jsc.2014.09.02268:P1(316-325)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1016/j.jsc.2014.09.022
Lebreton R(2015)Relaxed Hensel lifting of triangular setsJournal of Symbolic Computation10.1016/j.jsc.2014.09.01268:P2(230-258)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1016/j.jsc.2014.09.012
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